The present invention relates generally to a method of analyzing the characteristics of an underground reservoir. More particularly, the present invention deals with a method of reservoir analysis which utilizes type curve analyses.
In the petroleum industry, it is desirable to know many of the characteristics of the subterranean reservoir from which crude petroleum is being produced. These characteristics make it possible to predict with greater accuracy the length of time that a particular formation will produce and the volume of production that can be expected from that well during that period of time.
Many various theoretical models for underground reservoir formations have been developed by persons in the petroleum industry as well as others having an interest in the theory of reservoir fluid flows. The theoretical models of the past have been of significant value in beginning the systematic evaluation and analysis of existing wells as well as new wells. One of the important contributions of these various systematic analyses has been the development of type curves as a mechanism for determining reservoir characteristics.
Type curves are created in a dimensionless form for a particular theoretical model. Frequently, wellbore pressure is divided by the product of a group of reservoir parameters having the dimensions of pressure to obtain a dimensionless pressure. In similar fashion, time is divided by the product of a different group of reservoir parameters having dimensions of time to obtain a dimensionless time. The dimensionless pressure is graphically expressed as a function of the dimensionless time on the type curve while one or more other groups of reservoir parameters are held constant. In some analyses, the logarithm of dimensionless pressure and the logarithm of dimensionless time are presented in graphic form as the type curve.
Measurement data are then taken of particular characteristic parameters such as wellbore pressure as a function of time. Alternatively, the measurement data may represent data which had been takn at an earlier time. In both cases, the data are plotted in a particular form to a predetermined scale. When the plotted data is compared to the theoretical type curves by overlaying the plotted data on the theoretical type curve, information on the reservoir characteristics can be determined from the type curve which is most similar to the experimental data and, in some cases, from the displacement of the ordinate and abscissa of the experimental data from the ordinate and abscissa of the theoretical type curve.
Initially, the theoretical models used for the underground reservoir were relatively limited by current standards. An early concept on the pressure transient behavior of dual porosity media was presented by G. E. Barenblatt, I. P. Zheltov and I. N. Kochina, "Basic Concepts in the Theory of Homogeneous Liquids in Fissured Rocks", J. Applied Mathematical Mechanics (USSR) 24 (5) (1960) 1286-03. An idealized model representing flow in a naturally fractured (or vugular) reservoir was presented by J. E. Warren and P. J. Root, "The Behavior of Naturally Fractured Reservoirs", Society of Petroleum Engineering Journal, (Sept. 1963) 245-55; Transactions, AIME, 228. Warren and Root observed that the pressure behavior of a well producing from a dual porosity reservoir is influenced by two parameters, lambda and omega. These two parameters provide a measure of the fractures relative to the total volume and a measure of the production from the matrix. The Warren and Root mathematical model implies pseudo-steady state interaction between fractures and matrix in the underground formation. Such pseudo-steady state interaction results in an instantaneous pressure drop throughout the matrix when the fractures are depleted. Clearly, such a pseudo-steady state interaction does not closely resemble the natural effect of fracture depletion, namely, gradual pressure reduction.
The Warren and Root analysis has been followed by others working in the field of reservoir analysis. For example, the Warren and Root analysis is followed by D. Bourdet and A. C. Gringarten, "Determination of Fissure Volume and Block Size in Fractured Reservoirs by Type Curve Analysis", SPE 9293 presented at 1980 SPE Annual Technical Conference and Exhibition, Dallas, September 21-24. Type curves developed by Bourdet and Gringarten allow analysis of transient data from naturally fractured reservoirs.
In addition to the use of a dimensionless pressure, the first derivative of the dimensionless pressure taken with respect to dimensionless time has been used as a type curve in a pseudo-steady state reservoir analysis, see D. Bourdet, J. A. Ayoub, and Y. M. Pirard, "Use of Pressure Derivative in Well Test Interpretation", SPE 12777 (April 11-13, 1984). See also D. Bourdet, T. Whittle, A Douglas, and Y. M. Pirard, "New Type-Curves for Tests of Fissured Formations", World Oil (April 1984); U.S. Pat. No. 4,597,290.
The first derivative of dimensionless pressure taken with respect to dimensionless time has been used as a discriminant in reservoir analysis for quite some time. For example, D. Tiab and A. Kumar, "Application of the P'.sub.D Function to Interference Analysis", J. Petroleum Technology 1465-70 (August 1980) (dimensionless pressure derivative used in well interference analysis); S. K. Puthigai, "Application of P'.sub.D Function to Vertically Fractured Wells--Field Cases", SPE 11028 (Sept. 26-29, 1982) (dimensionless pressure derivative used for vertically fractured wells); D. Tiab and A. Kumar, "Detection and Location of Two Parallel Sealing Faults Around a Well", Journal of Petroleum Technology 1701-08 (October 1980) (dimensionless pressure derivative used for locating well relative to vertical fluid barriers).
Even when the pseudo-steady state model is modified to accommodate wellbore storage and skin effects, the resulting type curves are not entirely adequate. For example, the assumption of pseudo-steady state permits some of the interactive effects to be decoupled from other effects. This facet of the problem can be seen from the type curves used in U.S. Pat. No. 4,597,290 to Bourdet et al. In the Bourdet et al patent, not only are there a set of type curves for the dimensionless pressure derivative, there are two additional sets of type curves superimposed on the dimensionless pressure derivative curves that are necessary to determine the formation porosity characteristics of lambda and omega.
A mathematical model which does not suffer from an instantaneous pressure drop throughout the matrix when the fractures are depleted has been proposed by O. A. DeSwaan, "Analytical Solutions for Determining Naturally Fractured Reservoir Properties by Well Testing", Society of Petroleum Engineers Journal, 117-22 (December 1969), and extended by K. V. Serra, A. Reynolds, and R. Raghavan, "New Pressure Transient Analysis Methods for Naturally Fractured Reservoirs", J. Petroleum Technology 2271-83 (Dec. 1983). The DeSwaan model provides an unsteady state interaction between the matrix and the fractures. In such an interaction, pressure response throughout the matrix occurs transiently as the fractures are depleted.
In real wells, however, there are additional characteristics which affect the pressure response as a function of time. For example, when a well is drilled, the drilling mud tends to clog the porous structure immediately adjacent to the wellbore. That clogging is known in the industry as a skin effect. This skin effect is localized to the immediate vicinity of the wellbore itself and has the effect of creating resistance to the flow of fluid being produced.
Another aspect of real wells is known in the industry as the wellbore storage effect. This effect is a result of fluid loading, unloading, compressing, and/or expanding in the wellbore following a change to the production flow rate. This effect becomes more significant in well tests where the placement of the valve controlling fluid flow is at the surface.
It should now be apparent that there continues to be a need for a method of analyzing the transient behavior of underground reservoirs which compensates for effects such as wellbore storage, skin effects, double porosity reservoirs, and which accomplishes these things using an unsteady analysis scheme.